A Simple Visual Proof of the
The area of a square of side a + b is (a + b)2 or a2 + b2 + 2ab (I).
On the other hand, if the interior of the square is divided up into a square of side c and four right-angled triangles of sides a, b as shown below, its area equals the sum of the areas of these five figures, that is c2 + 4(ab/2) or c2 + 2ab (II).
Since the expressions (I) and (II) represent the same area, we have
a2 + b2 + 2ab = c2 + 2ab, which implies
a2 + b2 = c2